By inverse chronogical order of preparation (older first):
S.M. Gusein-Zade, I. Luengo, A. Melle-Hernández, and A. Viruel, "On the universal and generalized orbifold Euler characteristics" [arXiv]
A. Ceres, C. Costoya, and A. Viruel, "Hom-counting functions, combinatorial categories and related problems" [arXiv]
C. Costoya, R. Gomes and A. Viruel, "Rigidifying simplicial complexes and realizing group actions" [arXiv]